If I sample a large number of uniform points in the unit square and take a traveling salesman tour of them, is there anything at all that can be said/is known about the distribution of *angles* at each point? The two pictures below show a TSP tour of 1000 points, together with a histogram of the angles.

It is intuitive that we expect a lot of angles to be near $\pi$, since an angle close to $0$ (or to $2\pi$) suggests that we're "doubling back" on a route and possibly being inefficient.

Dubins' TSP: visiting the points by a vehicle that can only move forward and has a limited turning radius. In some sense, constraining the angle histogram. $\endgroup$